Modified 3D Massive Abelian 2-From Theory with a Single Pseudo-Scalar Field as a Phantom Field: BRST Approach

Abstract

We obtain the off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations (corresponding to the infinitesimal classical gauge symmetry transformations) for the modified massive three $(2+1)$-dimensional (3D) Abelian 2-form gauge theory with a single pseudo-scalar field. The latter field (having the negative kinetic term and a well-defined mass) has already been shown (i) to exist in the modified version of the standard 3D St$\ddot{u}$ckelberg formalism (on the solid mathematical grounds), (ii) to be a possible candidate for the ``phantom" field of some of the cosmological models of the Universe, and (iii) to be a possible candidate for dark matter. A couple of highlights of our present endeavor are (i) the observation that, even though the pseudo-scalar field does not transform under the gauge and (anti-)BRST symmetry transformations, it appears in the first-class constraints which annihilate the physical states at the quantum level, and (ii) the Noether conserved (anti-)BRST charges are found to be non-nilpotent. In our present investigation, we derive (i) the coupled (but equivalent) BRST and anti-BRST invariant Lagrangian densities, (ii) the conserved and off-shell nilpotent versions of the (anti-)BRST charges and the conserved ghost charge, (iii) the (anti-)BRST invariant Curci-Ferrari (CF) type restrictions, and (iv) the standard BRST algebra amongst the conserved and nilpotent (anti-)BRST charges and conserved ghost charge of our theory.

LaTeX file, 37 pages, version to appear in AHEP

References in corpus (21)

• A Cyclic Model of the Universe
• The Stueckelberg Field
• Ekpyrotic and Cyclic Cosmology
• Constructing stabilized brane world models in five-dimensional Brans-Dicke theory
• Ghosts in the self-accelerating universe
• Higher-Spin Gauge Theories and Bulk Locality
• Measurements, errors, and negative kinetic energy
• Bouncing cosmologies with dark matter and dark energy
• Energy conditions and current acceleration of the universe
• Higher Spin Gauge Theories in Any Dimension
• New topological field theories in two dimensions
• BRST, anti-BRST and their geometry
• Abelian p-Form (p = 1, 2, 3) Gauge Theories as the Field Theoretic Models for the Hodge Theory
• Modified 2D Proca Theory: Revisited Under BRST and (Anti-)Chiral Superfield Formalisms
• A Massive Field-Theoretic Model for Hodge Theory
• A Cyclic Universe Approach to Fine Tuning
• Noether Theorem and Nilpotency Property of the (Anti-)BRST Charges in the BRST Formalism: A Brief Review
• A 3D Field-Theoretic Example for Hodge Theory
• Modified St$\ddot{u}$ckelberg Formalism: Free Massive Abelian 2-Form Theory in 4D
• Constraints, Conserved Charges and Extended BRST Algebra for a 3D Field-Theoretic Example for Hodge Theory
• Pseudo-Scalar Field as a Possible Candidate for Phantom Field

Cited by in corpus (1)

• Nilpotency Property, Physicality Criteria, Constraints and Standard BRST Algebra: A 4D Field-Theoretic System